Pyramid Solitaire: pairs to 13 from a single deck
Pyramid is a one-deck game through and through. Its whole idea, removing two cards that add up to 13, depends on the exact makeup of a 52-card deck: four 6s to pair with four 7s, four Jacks with four 2s, four Queens with four Aces, and four Kings that go alone. Twenty-eight cards sit face up in a seven-row triangle, and 24 more wait in the stock, with three passes on this site. Clear the triangle to win.
Because every rank has exactly four partners, a single buried card can strand its match. A solver that plans every removal and knows the stock order proved 62.2% of 4,000 deals winnable (95% range 60.6%–63.6%), proved 14.0% impossible and ran out of budget on 23.9%. A greedy program that sees only face-up cards won 25.2% (23.9%–26.5%). There is no two-deck Pyramid on this site and we did not simulate one.
At a glance: one deck, four partners per rank
| Measure (one 52-card deck, 3 passes) | Result | 95% range | Deals |
|---|---|---|---|
| Solver, stock known: proven winnable | 62.2% | 60.6–63.6% | 4,000 |
| Solver: proven impossible | 14.0% | 12.9–15.1% | 4,000 |
| Solver: undecided | 23.9% | 22.6–25.2% | 4,000 |
| Greedy program, face-up cards only: won | 25.2% | 23.9–26.5% | 4,000 |
| At least one King in the top three rows | 40.8% | 39.3–42.3% | 4,000 |
| No King or pair available at the start | 3.6% | 3.0–4.2% | 4,000 |
With three passes, the winnable share lies between 62.2% and 86.0% for a player who knows the stock. The greedy figure is a floor. No published study we use covers Pyramid.
What one deck means for pairing
In a two-deck game, a card you need usually has a twin somewhere. Our Klondike program won 42.3% of one-deck deals and 81.5% of two-deck Solitaire Double deals (80.7–82.2%, 10,000 deals), largely because of those spares. Pyramid has none. If three 7s are already gone and the fourth sits under the 6 you want to clear, that 6 cannot leave. Spotting these locks early is the heart of Pyramid planning.
The passes are your only extra room. With one pass instead of three, the solver proved only 7.3% winnable (6.5%–8.1%) and 34.8% impossible (33.4%–36.3%), with 57.9% undecided. That run used a smaller budget (200,000 positions instead of 1,000,000), so the comparison is not exact.
Pyramid rules on this site
- Deck: one standard 52-card deck.
- Triangle: 28 face-up cards in seven rows; a card is free when nothing below covers it.
- Stock: 24 cards, turned one at a time to a waste pile, three passes in all.
- Pairs: two free cards totaling 13 (Ace 1, Jack 11, Queen 12).
- Kings: removed alone.
- Stock and waste: the top waste card can pair; from our reading of the code, so can the face-up top stock card.
- Win: clear the triangle.
Playing a deck with no spares
Track the four of each rank
Before you pair a 5 with an 8, count the 8s left. If the only other 8 is buried under a 5 you still need, that pairing may cost you later.
Choose the card that opens more
When two 7s could match your 6, take the one that frees more cards above it. The greedy program takes the first it finds.
High Kings set your route
In 40.8% of deals a King sat in the top three rows. Clear the side under it first.
Save a stock card for its only partner
If a stock card is the last partner for a buried triangle card, let it go by and use it on the next pass.
Undo stands in for the solver's knowledge
You can't see the stock, but you can try a line and take it back.
Playing on freecell-two-decks.com
Pyramid is free in any current browser on computer, tablet or phone, with no account. Hint, unlimited Undo, Restart and Auto Play are included, with zoom, fullscreen, drag or tap moves, a counter for wins, time and moves, and sound and table-color settings.
How the figures were made
The freecell-two-decks.com team ran these tests in September 2026 on this site's Pyramid rules, in Python 3.11 with the standard library only.
- Rules from the code: 28-card triangle, 24-card stock, three passes, pairs to 13, Kings alone. We assumed, from the code, that the face-up stock card can be paired directly.
- Deals 1 to 4,000 from fixed seeds, the same deals for every test.
- Two players: a greedy program on face-up cards only, and a solver that knows the stock (1,000,000 positions per deal for three passes, 200,000 for one pass). The solver drops a line as soon as a triangle card has no partner left anywhere.
- No two-deck Pyramid and no published figure. Blake and Gent (2026) do not cover Pyramid.
- 95% ranges: Wilson score intervals.
Claude, an AI assistant by Anthropic, helped write and review the code and draft this page. Every figure comes from running the code, and the team checked them.
Pyramid questions
Are some deals impossible?
Yes. 14.0% were proven impossible even with the stock known.
How many passes do I get?
Three on this site.
Is there a two-deck Pyramid?
No. For two-deck play, try FreeCell Two Decks or Solitaire Double.
What is similar?
Golf is the other quick one-deck game here. Every game is on the games page.
By Admin, freecell-two-decks.com (Forty Media). Research run September 2026.